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<p><dfn class="terminology">Analytic at a Point</dfn>   A function <span class="process-math">\(f\)</span> is <dfn class="terminology">analytic at a point <span class="process-math">\(x_0\)</span></dfn> if it can be represented by a power series in <span class="process-math">\(x-x_0\)</span> with a positive or infinite radius of convergence (i.e. <span class="process-math">\(\rho&gt;0\)</span>).In calculus, functions like <span class="process-math">\(e^x\text{,}\)</span> <span class="process-math">\(\cos(x)\text{,}\)</span> <span class="process-math">\(\sin(x)\)</span> can be represented by Taylor series with <span class="process-math">\(|x|&lt;\infty\text{.}\)</span></p>
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